Which of the following rewritten logarithms uses the Power Rule of Logarithms to evaluate log \( 8^{\frac{3}{4}} \) \( \frac{3}{4} \log 8 \) \( -\frac{4}{3} \log 8 \) \( -\frac{3}{4} \log 8 \) \( \frac{4}{3} \log 8 \)
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To rewrite the logarithm using the Power Rule, we take the exponent of the argument and multiply it by the logarithm of the base. The Power Rule states that \( \log_b(a^n) = n \cdot \log_b(a) \). Therefore, for \( \log 8^{\frac{3}{4}} \), we can rewrite it as \( \frac{3}{4} \log 8 \). That brings us to the correct choice: \( \frac{3}{4} \log 8 \), which is a straightforward application of the Power Rule! Now, isn't it fun to see how one little rule can simplify our lives when dealing with logarithms?
